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05 Apr 2024, 01:31
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
78% (02:02) correct
22%
(02:40)
wrong
based on 173
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On average, each member of Team B earned 3/5 as much as each member of Team A last year. If Team B has 3/4 as many members as Team A, what fraction of the total earnings did Team A earn?
A. 1/4
B. 7/12
C. 3/5
D. 5/8
E. 20/29
A. 1/4
B. 7/12
C. 3/5
D. 5/8
E. 20/29
05 Apr 2024, 03:25
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The fraction of the total earnings that Team A's earned will be: \(\frac{TeamA earnings}{TeamA earnings + TeamB earnings}\)
On average, each member of Team B earned 3/5 as much as each member of Team A last year: \(x = 1\) & \(y = \frac{3}{5}\)
where x and y denote the average income of Team A and B, respectively.
Team B has 3/4 as many members as Team A: \(a = 1\) & \(b = \frac{3}{4}\)
To get the total earnings of each group, one multiplies the average earnings of each group with the number of members in their respective groups.
Team A earnings: \(1*1 = 1\)
Team B earnings: \(\frac{3}{5}*\frac{3}{4} = \frac{9}{20}\)
Plugging these values back into \(\frac{TeamA earnings}{TeamA earnings + TeamB earnings}\):
\(\frac{1}{1+\frac{9}{20}}\)
\(\frac{1}{\frac{29}{20}}\)
\(\frac{20}{29}\)
ANSWER E
On average, each member of Team B earned 3/5 as much as each member of Team A last year: \(x = 1\) & \(y = \frac{3}{5}\)
where x and y denote the average income of Team A and B, respectively.
Team B has 3/4 as many members as Team A: \(a = 1\) & \(b = \frac{3}{4}\)
To get the total earnings of each group, one multiplies the average earnings of each group with the number of members in their respective groups.
Team A earnings: \(1*1 = 1\)
Team B earnings: \(\frac{3}{5}*\frac{3}{4} = \frac{9}{20}\)
Plugging these values back into \(\frac{TeamA earnings}{TeamA earnings + TeamB earnings}\):
\(\frac{1}{1+\frac{9}{20}}\)
\(\frac{1}{\frac{29}{20}}\)
\(\frac{20}{29}\)
ANSWER E
General Discussion
07 Apr 2024, 11:56
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Plugging in values :
Let each member of Team A earn 100, which means each member of Team B will earn 3/5 * 100 = 60
Assuming there are 12 members on Team A, which means Team B will have 3/4 * 12 = 9
Total earnings of Team A = 100*12 = 1200
Total earnings of Team B = 60 * 9 = 540
Overall earnings of both teams = 1200 + 540 = 1740.
Fraction of Team A's total earnings will be 1200/1740 = 20/29
ANSWER E
Let each member of Team A earn 100, which means each member of Team B will earn 3/5 * 100 = 60
Assuming there are 12 members on Team A, which means Team B will have 3/4 * 12 = 9
Total earnings of Team A = 100*12 = 1200
Total earnings of Team B = 60 * 9 = 540
Overall earnings of both teams = 1200 + 540 = 1740.
Fraction of Team A's total earnings will be 1200/1740 = 20/29
ANSWER E
